The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  1  X  1  1  X  1  1 X^2  2  X  1  1  1  1  1  1  1  1  1 X^2+X+2 X^2  1 X^2+2  1 X+2  1  0  1  0  1  1  1  1 X^2+X+2  1  1 X^2+X+2  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+3 X^2+X+1  1 X^2+2  X  1  X X+1  1  1  1 X^2+X+3 X^2+1  0 X^2+2 X+3 X^2+2 X+2 X^2+X+2 X+1  1  1  X  1  3  1 X^2+X  1 X^2+2  1  X X^2+3  X X^2+3  1 X^2+2 X^2+X+3  1  3  3  1
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2  X X^2+2  X  0 X^2+X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2  2  0 X+2 X^2+X X^2+X X^2 X^2+X+2 X^2+2 X^2+2  X  2  2 X^2+2 X^2 X^2+X+2 X^2+X X^2+X+2 X^2+X X^2+2 X+2  X X^2+2  0 X^2+X  2 X^2+X+2  2  2  0  2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  2  0  2  2  0  2  2  2  0  0  0  2  0  0  0  0  2  0  0  2  0  0  0  0  0  0  2

generates a code of length 60 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+287x^56+416x^57+678x^58+352x^59+759x^60+352x^61+564x^62+416x^63+189x^64+30x^66+33x^68+8x^70+8x^72+3x^80

The gray image is a code over GF(2) with n=480, k=12 and d=224.
This code was found by Heurico 1.16 in 0.344 seconds.